JEEAdvanced
Find the number of ordered pairs of positive integers (a, b) such…
Question
Find the number of ordered pairs of positive integers (a, b) such that lcm(a, b) = 600.
✓ Verified answer: 105checked by our engine — not a guess
Step-by-step solution
600 = 2^3 · 3^1 · 5^2.
For lcm(a,b)=600, write a = 2^x1·3^y1·5^z1, b = 2^x2·3^y2·5^z2.
For each prime we need max of the two exponents to equal the exponent in 600.
For exponent E, the number of ordered pairs (i,j) with 0≤i,j≤E and max(i,j)=E is 2E+1.
So for prime 2 (E=3): 7 pairs; prime 3 (E=1): 3 pairs; prime 5 (E=2): 5 pairs.
Total = 7·3·5 = 105.
Final answer105
Stuck on a problem like this?
Paste any JEE or NEET question — verified working, a confidence %, and an honest “not sure” instead of a bluff.
Solve my doubt →More Number Theory solutions
Find the remainder when the power tower 7^(7^7) is divided by 1000.…JEE · MathHow many trailing zeros does 2026! have when it is written in base…JEE · MathA positive integer is called 'rough' if it is divisible by the square…JEE · MathLet D be the set of all positive divisors of 2025. Compute the sum of…JEE · MathConsider repdigit numbers made entirely of the digit 8, i.e. 8, 88,…JEE · MathLet sigma(n) denote the sum of all positive divisors of n. Count the…JEE · MathFind the number of integers x with 0 ≤ x < 18000 satisfying x^2 ≡ 1…JEE · MathCompute the value of the sum S = sum_{k=1}^{100} k · gcd(k, 100).JEE · Math